As shown below, the stellar velocity dispersion (\(\sigma _*\) ) for AGNs is
systematically different from other galaxies of the same stellar mass.
We thus also construct control samples according to \(\sigma _*\) .
The values of \(\sigma _*\)  are also taken from the NYU-VAGC and corrected
to the same effective aperture using the formula of [1]}.
The control samples, cSF\(^{\rm c2}_{\sigma _*}\)  and cQ\(^{\rm c2}_{\sigma _*}\) ,
are constructed, respectively, from the star-forming and quiescent
galaxies with \(\sigma _*\)  measurements, by matching redshift, \(M_*\)  and
\(\sigma _*\) . The tolerance in \(\sigma _*\)  is \(\mid \Delta \sigma _{*}\mid <\)  20\(\,{\rm {km\, s^{-1}}}\) .
Some AGNs have no \(\sigma _*\)  measurements and/or no matched galaxies.
Excluding these galaxies results in 43,851 central AGNs, and this
new AGN sample is referred to as cAGN\(_{\sigma _*}\) . For comparison,
we also construct another set of control samples, cSF\(^{\rm c}_{\sigma _*}\) 
and cQ\(^{\rm c}_{\sigma _*}\) , for cAGN\(_{\sigma _*}\) , by only matching
stellar mass and redshift.
